The introductory-level formula for motional EMF can be obtained a number of different ways. It is instructive to lead students through the different derivations in the following specific sequence, because each method brings out a different important aspect of the situation. The first three ways can be used with majors and non-majors alike. The last approach is optionally for physics majors who have been exposed to the idea that a magnetic field is an electric field viewed in a moving reference frame.
(1) Apply Faraday's law to a conducting bar sliding on a U-shaped wire.
(2) Use work to calculate the change in electrostatic PE of mobile charges driven along a conducting bar moving in a magnetic field.
(3) Consider the balance between the applied and magnetic-braking powers as a conducting bar slides on a U-shaped wire at constant velocity. As a bonus, verify Lenz's law.
(4) Compute the emf as the integral of the electric field in the bar's frame which is the transform of the magnetic field in the lab frame.